Changes in the elevation and extent of the Antarctic icesheet have an important role in modulating global atmospheric and oceanographic processes, and contribute significantly to world-wide sea levels. This report summarizes results of a numerical study on the response of the Antarctic ice sheet to changes in environmental conditions, both on the longer palaeoclimatic time scale (104-105 y) as on the shorter time scale (10² y) associated with future greenhouse warming. The ice sheet model developed to this aim is three-dimensional and time-dependent. It incorporates a coupled ice shelf, grounding-line dynamics, basal sliding and isostatic bed adjustment. Ice flow is calculated on a fine mesh (40 km horizontal grid size and 10 layers in the vertical) for grounded and floating ice and a stress transition zone in between, where all stress components contribute in the effective stress of the flow law. The model has a full coupling between thermal field and ice flow and the ice sheet geometry is freely generated in response to changes in sea level, surface temperature and mass balance. The mass-balance model consists of two parts: the accumulation rate is derived from present observed values and is consequently perturbed in proportion to the saturated vapour pressure at the temperature above the inversion layer. The ablation-and-runoff model required for warmer climates is based on the degree-day method. It accounts for the daily temperature cycle, uses a different degree-day factor for snow and ice melting and treats refreezing of melt water in a simple way. A simulation of the present ice sheet reveals that the model is able to yield realistic results. An attempt is then made to simulate the ice sheet through the last glacial-interglacial cycle. To do this, the Vostok temperature record is used to force changes of both surface temperature and accumulation rate and sea level is prescribed by a piecewise linear sawtooth function. In line with glacial-geological evidence, the most pronounced changes occur in the West Antarctic ice sheet configuration. These fluctuations are essentially controlled by variations in eustatic sea level, whereas typical glacial- interglacial changes in temperature and ice deposition rates tend to balance one another. These findings support the hypothesis that the Antarctic ice sheet basically follows glacial episodes in the northern hemisphere by means of sea-level teleconnections. On the shorter greenhouse warming time scale, the model's response is determined by changes in the mass balance. It is found that as long as the temperature rise is below 5°C, the Antarctic ice sheet is likely to grow, because melting at the ice sheet edge can still be offset by higher deposition rates on the plateau. These model results do not support the hypothesis of a catastrophic collapse of the West Antarctic ice sheet, not even when a uniform melting rate of 1 m/year is imposed below the ice shelves.